This work presents an x-ray absorption measurement by use of ionizing radiation generated by a femtosecond pulsed laser source. The spectrometer was a microcalorimetric array whose pixels are capable of accurately measuring energies of individual radiation quanta. An isotropic continuum x-ray spectrum in the few-keV range was generated from a laser plasma source with a water-jet target. X rays were transmitted through a ferrocene powder sample to the detector, whose pixels have average photon energy resolution ΔE=3.14 eV full-width-at-half-maximum at 5.9 keV. The bond distance of ferrocene was retrieved from this first hard-x-ray absorption fine-structure spectrum collected with an energy-dispersive detector. This technique will be broadly enabling for time-resolved observations of structural dynamics in photoactive systems.